Nested odd repetition proportion controller and design method thereof

Abstract

The invention discloses a nested odd repetition proportion controller and a design method thereof. The design method comprises the following steps: S1, determining a transfer function of a controlled object; s2, constructing a nested odd repetitive control internal model; the nested odd repetitive control internal mold comprises an external odd repetitive control internal mold and an internal odd repetitive control internal mold which are arranged in a nested manner; s3, compensating the nested odd repetition control internal model by adopting a system compensator and a phase lead compensator so as to construct a nested odd repetition controller; s4, aiming at the controlled object, adding a feedforward controller to the nested odd repetition controller to obtain a nested odd repetition proportional controller; and S5, designing and selecting nested odd repetition proportion control parameters to form a stable nested odd repetition proportion control system. According to the invention, high gain capability is realized at odd harmonics, repeated control of even harmonics can be suppressed, and harmonic suppression capability and strong robustness when power grid frequency fluctuates are improved.

Description

Technical Field

[0001] The present invention belongs to the field of industrial control, and in particular relates to a nested odd-order repetitive proportional controller and a design method thereof. Background Art

[0002] With the rapid development of new energy technologies, modern power systems are gradually shifting from high-inertia systems such as traditional thermal power generators to renewable energy generation systems. As a core component of distributed power generation systems, the quality of grid-connected inverter output power is directly related to the reliability and stability of grid operation. In this context, grid background harmonics generated by the imbalance between generated power and load power not only distort the grid current but also cause grid frequency fluctuations, reducing system stability and posing a severe challenge to the stable and efficient operation of grid-connected inverters. The total harmonic distortion (THD) of the grid-connected inverter output current is a key indicator for evaluating the quality of the power injected into the grid by the grid-connected inverter. The THD of the grid-connected current should be less than 5%. Therefore, to improve the operational reliability and stability of weak grids in complex environments, research on grid-connected inverter control strategies with strong robustness and high steady-state performance is crucial for the stable operation of the system.

[0003] In order to suppress low-frequency harmonics in grid-connected inverters, quasi-proportional resonant control (QPR) is generally adopted. However, the parallel connection of multiple quasi-resonant controllers proposed by this control strategy easily makes the system parameter design complicated, resulting in poor system stability. Repetitive control (RC) has been widely used in inverter control systems because it can track the fundamental periodic signal without static error and suppress the harmonic disturbance of the double frequency. In 2024, G. Zhang et al. published an article entitled "Feedforward Repetitive Control for Grid-Tied Inverters in Microgrids: Analysis, Design, and Verification" in the Journal of Electrotechnical Engineering. The article records the internal model structure of traditional repetitive control (RC) and odd-repetitive control (ORC), such as Figure 1 and Figure 2Compared with traditional repetitive control (RC), odd-order repetitive control (ORC) not only has a simple structure, but also can increase the resonant bandwidth of repetitive control and improve the frequency robustness of the repetitive control system. However, it only has high gain characteristics at odd harmonics and has no suppression ability for even harmonics. When the sampling frequency is 10kHz, the open-loop Bode diagrams of RC and ORC are shown as follows: Figure 3 As shown. Figure 3 It can be seen that the bandwidth of ORC at the resonant frequency is wider than that of RC, and it has stronger frequency robustness. However, ORC loses the ability to suppress even harmonics. Therefore, the ORC solution still needs to be improved.

[0004] Therefore, it is necessary to study a controller that can have high gain capability at odd harmonics and suppress even harmonics to improve the stable operation capability of the control system. Summary of the Invention

[0005] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, to achieve a repetitive controller with high gain capability at odd harmonics while suppressing even harmonics, and to provide a nested odd-order repetitive proportional controller and a design method thereof.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A nested odd-order repetitive proportional controller design method comprises the following steps:

[0008] S1: Determine the transfer function P(s) of the controlled object;

[0009] S2: Construct nested odd-order repetitive control internal model;

[0010] The nested odd-repetition control internal model includes an external odd-repetition control internal model and an internal odd-repetition control internal model that are nested. The internal odd-repetition control internal model G iorc (z) Insert the odd repetition control inner model G in the outer norc (z), its expression is:

[0011]

[0012] Among them, γ1 and γ2 are the first internal model coefficient and the second internal model coefficient of the internal odd-order repetitive control internal model, k r is the internal model gain;

[0013] S3: Add a phase lead compensator and a system compensator to the nested odd-order repetitive control internal model to construct a nested odd-order repetitive controller, whose discrete transfer function G2(z) is:

[0014]

[0015] Among them, z m is the phase advance compensator, S(z) is the system compensator;

[0016] S4: Add a feedforward controller to the nested odd-order repetitive controller G2(z) for the controlled object P(s) to obtain a nested odd-order repetitive proportional controller, whose output y(z) is expressed as follows:

[0017]

[0018] Among them, r(z) is the reference signal, d(z) is the disturbance signal, k p is the proportional gain of the feedforward controller, P(z) is converted from P(s) using the zero-order hold method;

[0019] The transfer function P0(z) of the controlled object under the control of the feedforward controller is expressed as:

[0020]

[0021] S5: Design and select nested odd-repetition proportional control parameters to form a stable nested odd-repetition proportional control system, that is, the characteristic equation of the nested odd-repetition proportional control system (1+k p P(z))(1+G2(z)P0(z)) satisfies the first stability condition and the second stability condition,

[0022] The first stability condition is: 1+k p All roots of P(z) are inside the unit circle centered at the origin;

[0023] The second stability condition is: |1+G2(z)P0(z)|≠0.

[0024] The nested odd-order repetitive control internal model of the present invention adjusts the external odd-order repetitive control gain through the internal odd-order repetitive control internal model, so as to achieve a higher gain of the controller at the odd resonant frequency and better suppression of odd harmonics. At the same time, it also has a certain gain effect at the even resonant frequency, thereby achieving the effect of suppressing even harmonics.

[0025] Preferably, the proportional gain k in step S4 is p The method to determine is:

[0026] Selecting a proportional gain value within a preset proportional gain range, and constructing a Bode diagram of the transfer function P0(z) of the controlled object under the control of the feedforward controller corresponding to different proportional gain values;

[0027] Determine the proportional gain k when the first stability condition is met based on the Bode diagram p .

[0028] By connecting the nested odd-order repetitive controller and the feedforward controller in parallel, the dynamic response speed of the system can be increased and the dynamic performance can be improved.

[0029] Preferably, the internal odd repetition control internal model G iorc The method to determine is:

[0030] Select the first internal model coefficient value within the preset first internal model coefficient range, select the second internal model coefficient value within the preset second internal model coefficient range, and construct the G corresponding to different first internal model coefficient values ​​and second internal model coefficient values. iorc The Bode plot of (z),

[0031] According to the Bode diagram, the first internal model coefficient γ1 and the second internal model coefficient γ2 are determined, and then the internal odd-order repetitive control internal model G is determined. iorc .

[0032] Preferably, the system compensator S(z) adopts a fourth-order Butterworth low-pass filter with a cutoff frequency of 1 kHz, and its transfer function is:

[0033]

[0034] Preferably, the step S5 further includes: obtaining the controller gain k according to the second stability condition r and phase lead compensator z m The condition of the parameter m, the controller gain k r The conditions are:

[0035]

[0036] The phase lead compensator z m The conditions for the parameter m are:

[0037] |θ s (w)+θ p (w)+mw|<90°.

[0038] Preferably, the phase lead compensator z m The method to determine is:

[0039] According to the phase advance compensator z m The conditions of the parameter m, constructing θ when different parameter m values s (w)+θ p The Bode diagram of (w)+mw is used to select the value of the parameter m.

[0040] Preferably, the controller gain k r The method to determine is: According to the second stability condition, let

[0041] H(z)=Q(z)(1-k r z m S(z)P0(z));

[0042] Where z = e jwt , according to the controller gain k r Under the conditions, different controller gains k are constructed r When H(e jwt ) Nyquist curve, and determine k according to the Nyquist curve r The value of .

[0043] Preferably, the controlled object is an industrial device whose output voltage / current signal is composed of odd-order characteristic power, including a programmable AC power supply, a power converter and a servo motor.

[0044] Preferably, the controlled object is an LCL filter, and the transfer function P(s) of the controlled object is:

[0045]

[0046] Among them, L1 is the filter inductor on the inverter side, L2 is the filter inductor on the grid side, C is the filter capacitor, and R is the damping resistor.

[0047] A nested odd-repetition proportional controller is provided. The controller is realized by the nested odd-repetition proportional controller design method.

[0048] The present invention adopts a nested odd-repetition proportional control strategy and sets an internal model formed by two odd-repetition controls, thereby improving the harmonic suppression capability and strong robustness in dealing with grid frequency fluctuations, breaking through the limitations of traditional control strategies in terms of harmonic suppression range, and significantly improving the system's stable operation capability under non-ideal conditions, providing a more excellent solution for grid-connected inverter control in complex grid conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The present invention is described in further detail below with reference to the accompanying drawings:

[0050] Figure 1 It is the internal model structure diagram of traditional repetitive control (RC);

[0051] Figure 2 It is the internal model structure diagram of odd repetitive control (ORC);

[0052] Figure 3 is the open-loop Bode plot of conventional repetitive control (RC) and odd-order repetitive control (ORC);

[0053] Figure 4 It is a single-phase LCL type grid-connected inverter circuit;

[0054] Figure 5 1 is a diagram of the internal model structure of the nested odd-order repetitive control internal model (NORC) of the method of the present invention;

[0055] Figure 6 is an open-loop Bode diagram of the internal odd-order repetitive control internal model of the method of the present invention;

[0056] Figure 7 are the open-loop Bode plots of conventional repetitive control (RC), odd-order repetitive control (ORC), and nested odd-order repetitive control internal model (NORC);

[0057] Figure 8 It is a structural diagram of the nested odd-repetition proportional controller of the method of the present invention;

[0058] Figure 9 is the different proportional gain k of the method of the present invention p The extreme point distribution of P0(z) under the value;

[0059] Figure 10 is the different proportional gain k of the method of the present invention p Bode diagram of P0(z) under the value;

[0060] Figure 11 is the G under different γ1 and γ2 values ​​of the method of the present invention iorc Bode plot of (z);

[0061] Figure 12 is the Bode plot of S(z)P0(z) and P0(z) of the method of the present invention;

[0062] Figure 13 is the value of different parameter m of the method of the present invention s (w)+θ p Bode plot of (w)+mw;

[0063] Figure 14 are the different controller gains k of the method of the present invention r When H(e jwt )’s Nyquist curve;

[0064] Figure 15 The THD of the grid-connected current of the conventional repetitive control (RC), odd-order repetitive control (ORC) and nested odd-order repetitive proportional control internal model (NORC-PC) of the method of the present invention at different grid frequencies f0 is compared;

[0065] Figure 16 is the grid-connected current and its spectrum of the traditional repetitive control (RC) when the grid frequency is f0 = 50 Hz;

[0066] Figure 17is the grid-connected current and its spectrum of odd-order repetitive control (ORC) when the grid frequency f0 = 50 Hz;

[0067] Figure 18 It is the grid-connected current and its spectrum of the nested odd-order repetitive proportional control internal model (NORC-PC) of the method of the present invention when the grid frequency f0=50Hz. DETAILED DESCRIPTION

[0068] The present invention provides a nested odd-repetitive proportional controller design method, which includes the following steps.

[0069] S1: Construct a single-phase LCL grid-connected inverter and determine the transfer function P(z) of the controlled object based on the single-phase LCL grid-connected inverter. The single-phase LCL grid-connected inverter includes an LCL filter, a phase-locked loop (PLL), and a current controller G i (z), PWM generator and inverter. The LCL filter includes the inverter side filter inductor L1, the grid side filter inductor L2, the filter capacitor C and the damping resistor R. The controlled object is the LCL filter;

[0070]

[0071] Single-phase LCL type grid-connected inverter such as Figure 4 As shown, where E d is the DC bus voltage, u inv is the inverter output voltage, i g is the grid-connected current, u g is the grid voltage, i c The phase-locked loop (PLL) is used to collect the phase of the voltage at the point of common coupling (PCC) of the power grid and the reference current I ref The amplitude of the reference current i ref , G i (z) is a current controller, which is used to control the on and off of the inverter bridge to achieve closed-loop control of the grid current. ZOH is a zero-order holder.

[0072] S2: Construct a nested odd-order repetitive control internal model (NORC); Figure 5 As shown, the nested odd-repetition control internal model includes an external odd-repetition control internal model and an internal odd-repetition control internal model set in a nested manner, and the internal odd-repetition control internal model G iorc (z) Insert the external odd repetition control inner model G norc (z), its expression is:

[0073]

[0074] Among them, γ1 and γ2 are the first internal model coefficient and the second internal model coefficient of the internal odd-order repetitive control internal model, k r is the internal model gain, and P(z) is converted from P(s) using the zero-order hold method. In this embodiment, the zero-order protection method uses a zero-order holder.

[0075] In this embodiment, the nested odd-order repetition control internal model can replace the traditional internal model filter Q(z), and the internal odd-order repetition control internal model G iorc (z) Adjust the external odd repetitive control gain by adjusting γ1 and γ2 to increase G iorc The amplitude-frequency characteristic of (z) is adjusted between 0 and 1, G iorc (z) Figure 6 As shown. Figure 6 It can be seen that G iorc (z) The gain at the odd resonant frequency is higher, and the odd harmonics are better suppressed. At the same time, there is also a certain gain effect at the even resonant frequency, thereby achieving the effect of suppressing the even harmonics.

[0076] In this embodiment, the open-loop Bode diagrams of the traditional repetitive controller (RC), odd-order repetitive controller (ORC), and nested odd-order repetitive control internal model (NORC) are as follows: Figure 7 As shown. Figure 7 It can be seen that the nested odd-order repetitive control internal model (NORC) has better frequency robustness than the RC at the fundamental frequency, while also having the ability to suppress even harmonics that the ORC lacks. Therefore, the nested odd-order repetitive control internal model (NORC) has stronger frequency robustness than the repetitive controller (RC) and more comprehensive harmonic suppression than the odd-order repetitive controller (ORC).

[0077] S3: Add a phase lead compensator and a system compensator to the nested odd-order repetitive control internal model to construct a nested odd-order repetitive controller, whose discrete transfer function G2(z) is:

[0078]

[0079] Among them, z m is the phase advance compensator, and S(z) is the system compensator.

[0080] S4: Add a feedforward controller to the nested odd-order repetitive controller G2(z) for the controlled object P(s) to obtain a nested odd-order repetitive proportional controller, as shown in Figure 8 As shown, the expression of its output y(z) is;

[0081]

[0082] Among them, r(z) is the reference signal, d(z) is the disturbance signal, kp is the proportional gain of the feedforward controller. In this embodiment, the reference signal r(z) is the reference current i ref , the disturbance signal d(z) is the grid current i g , NORC-PC is a nested odd-order repetitive proportional control internal model.

[0083] The transfer function P0(z) of the controlled object under the control of the feedforward controller is expressed as:

[0084]

[0085] In this embodiment, by connecting the nested odd-order repetitive controller G2(z) and the feedforward controller in parallel, the dynamic response speed of the system can be increased and the dynamic performance can be improved.

[0086] S5: Design and select nested odd-order repetitive proportional control parameters to form a stable nested odd-order repetitive proportional control system, that is, the characteristic equation of the nested odd-order repetitive proportional control system (1+k p P(z))(1+G2(z)P0(z)) satisfies the first stability condition and the second stability condition,

[0087] The first stability condition is: 1+k p All roots of P(z) are inside the unit circle centered at the origin;

[0088] The second stability condition is: |1+G2(z)P0(z)|≠0.

[0089] In this embodiment, the method for obtaining the characteristic equation of the nested odd-order repetitive proportional control system is:

[0090] According to the expression of the output y(z) of the nested odd-order repetitive proportional controller, the characteristic polynomial of the nested odd-order repetitive proportional control system is obtained as follows:

[0091] 1+(G2(z)+k p )P(z);(7)

[0092] Substitute the transfer function P0(z) of the controlled object under the control of the feedforward controller (6) into the characteristic polynomial formula (7) for transformation to obtain the characteristic equation:

[0093] 1+(G2(z)+k p )P(z)=(1+k p P(z))(1+G2(z)P0(z));(8)

[0094] The first stability condition and the second stability condition are obtained according to the characteristic equation.

[0095] Nested odd repetition ratio control parameters include: internal odd repetition control internal model G iorc The first internal model coefficient γ1 and the second internal model coefficient γ2, the parameters of the system compensator S(z), the controller gain k r , Phase Lead Compensator z m Parameters m and proportional gain k p .

[0096] In this embodiment, the proportional gain k p The method for determining is as follows: select a proportional gain value within a preset proportional gain range, construct a Bode diagram of the transfer function P0(z) of the controlled object under the control of the feedforward controller corresponding to different proportional gain values; determine the proportional gain k when the first stability condition is met based on the Bode diagram p .

[0097] Since the proportional gain k p It has a great influence on the stability of the system. Choosing a suitable k p The value can make the amplitude-frequency characteristic of P0(z) remain constant in the low frequency band, that is, to achieve the most ideal frequency characteristic of the controlled object of the nested odd-order repetitive proportional controller. According to the first stability condition, the system needs to satisfy 1+k p The root of P0(z)=0 is inside the unit circle, that is, the pole of P0(z) is inside the unit circle. p When the value is 8 to 12, the pole distribution and Bode diagram of P0(z) are as follows: Figure 9 、 Figure 10 As shown. Figure 9 It can be seen that k p When the value changes between 8 and 12, the poles are all inside the unit circle of the z plane. p The values ​​of k all meet the stability conditions. p The Bode diagram under the value of Figure 10 As shown. Figure 10 It can be seen that taking different k p When the value is set, the amplitude characteristics of the Bode diagram of P0(z) in the low frequency band will change. In order to keep the amplitude-frequency characteristics at a constant gain, the amplitude-frequency characteristics curve in the low frequency band should be kept as flat as possible, so here k p The value is 10.

[0098] In this embodiment, the internal odd repetition control internal model G iorc The determination method is as follows: select a first internal model coefficient value within a preset first internal model coefficient range, select a second internal model coefficient value within a preset second internal model coefficient range, and construct G corresponding to different first internal model coefficient values ​​and second internal model coefficient values. iorc (z) Bode diagram, the first internal model coefficient γ1 and the second internal model coefficient γ2 are determined according to the Bode diagram, and then the internal odd-order repetitive control internal model G is determined. iorc .

[0099] When selecting the first internal model coefficient γ1 and the second internal model coefficient γ2, it should be noted that in traditional repetitive control, the ideal internal model filter Q(z) = 1, but this often leads to system stability problems. To ensure system stability, γ1 and γ2 can be adjusted. Changing the values ​​of γ1 and γ2 can adjust G iorc Gain at odd harmonics and even harmonics. When making specific adjustments, G iorc (z) A significant high gain characteristic is formed at the odd harmonic frequency to ensure effective suppression of the target harmonics, while maintaining appropriate gain at the even harmonics to achieve the suppression effect of the even harmonics. iorc (z) Figure 11 In this embodiment, γ1 and γ2 are set to 5.62 and 0.145 respectively, which corresponds to the curve G iorc5 ,From the Bode diagram, it can be seen that the internal model filter at this time not only meets the requirements of ,the suppression of the main harmonics, but also effectively avoids the risk of system ,instability by retaining the limited suppression capability of the even harmonics, ,achieving a balance between control performance and system ,stability.

[0100] In this embodiment, the system compensator S(z) adopts a fourth-order Butterworth low-pass filter with a cutoff frequency of 1 kHz, and its transfer function is:

[0101]

[0102] The Bode diagram of the controlled object P0(z) under the control of the feedforward controller before and after adding the system compensator S(z) is as follows: Figure 12 As shown. Figure 12 It can be seen that the high-frequency attenuation capability of the system is greatly improved after the system compensator S(z) is added.

[0103] In this embodiment, step S4 further includes: obtaining the controller gain k according to the second stability condition r and phase lead compensator z m The conditions for the parameter m are as follows:

[0104] Substituting the discrete transfer function G2(z) of the nested odd-order repetitive controller into the second stability condition, we get:

[0105]

[0106] To satisfy formula (10), the first inequality condition must be met:

[0107] |G iorc (z)z -N / 2 (1-k r z mS(z)P0(z))|<1;(11)

[0108] The reference signal and the disturbance signal are set to be integer multiples of the fundamental frequency, i.e. |z N |=1, and then we substitute into formula (11):

[0109] |G iorc (z)(1-k r z m S(z)P0(z))|<1;(12)

[0110] According to the transfer function P0(z) of the controlled object under the control of the feedforward controller and the frequency characteristics of the system compensator S(z), we can obtain:

[0111]

[0112] Among them, N p (w) and θ p (w) are the amplitude-frequency characteristics and phase-frequency characteristics of P0(z), N s (w) and θ s (w) are the amplitude-frequency characteristics and phase-frequency characteristics of S(z) respectively.

[0113] z m By expanding the Euler formula, the formula for converting the z domain to the frequency domain is z = e jw , w is the normalized frequency, then:

[0114] z m =e jmw (15)

[0115] Let the internal odd repetitive control internal model G used for the internal model filter be iorc The value of (z) is 1, and formula (13), formula (14) and formula (15) are substituted into formula (12) to convert:

[0116]

[0117] That is, formula (12) is converted to:

[0118]

[0119] From Euler's formula, we can know that the exponential function e is expanded, because k r >0,N s (w)>0,N p (w)>0, let A=k r N s (w)N p (w), transform formula (16) into:

[0120] ‖1-A[cos(θs (w)+θ p (w)+mw)+jsin(θ s (w)+θ p (w)+mw)]‖<1;(17)

[0121] Let θ = θ s (w)+θ p (w)+mw, there is ‖1-Acosθ-jsinθ‖<1,

[0122] The formula for calculating the modulus of a complex number is:

[0123] Therefore, formula (17) is expanded to:

[0124]

[0125] (1-Acosθ) 2 +(Asinθ) 2 <1;

[0126] So we get: A 2 <2Acosθ;

[0127] Since A>0, A<2cosθ;

[0128] Right now:

[0129] |k r N s (w)N p (w)|<2cos[θ s (w)+θ p (w)+mw];(18)

[0130] Then we get the controller gain k r Conditions:

[0131]

[0132] and phase lead compensator z m The conditions for the parameter m are:

[0133] |θ s (w)+θ p (w)+mw|<90°. (20)

[0134] In this embodiment, the phase lead compensator z m The determination method is: according to the phase advance compensator z m The conditions of the parameter m, constructing θ when different parameter m values s (w)+θ pThe Bode diagram of (w)+mw is used to select the value of the parameter m.

[0135] In this embodiment, the phase lead compensator z m Used to compensate for the phase lag caused by the controlled objects P0(z) and S(z) under the control of the feedforward controller, especially the phase lag in the high-frequency area, the phase lead compensator z m For providing an angle θ=m(ω / ω N )°π advance angle, where ω N is the Nyquist frequency. s (w)+θ p (w)+mw Bode diagram Figure 13 As shown by Figure 13 It can be seen that when m=8, θ s (w)+θ p The phase of (w)+mw is closest to 0° within 1kHz, which meets the requirements of ideal stability conditions.

[0136] In this embodiment, the controller gain k r The method to determine is: According to the second stability condition, let

[0137] H(z)=Q(z)(1-k r z m S(z)P0(z));(21)

[0138] Where z = e jwt , according to the controller gain k r Under the conditions, different controller gains k are constructed r When H(e jwt ) Nyquist curve, and the controller gain k is determined according to the Nyquist curve r The value of .

[0139] In this embodiment, formula (12) means that if H(e jwt ) is inside the unit circle, then the system will converge asymptotically, and H(e jwt The closer the trajectory of ) is to the center of the circle, the greater the system stability margin. The controller gain k r The Nyquist curve corresponding to the change from 8 to 12 is as follows Figure 14 As shown. Figure 14 It can be seen that k r When the value of increases from 8 to 12, the system tends to be stable, but it can be seen that when k r =10, the low frequency segment of the Nyquist curve of the system is closer to the center of the circle, that is, the system has better reference signal tracking capability and low frequency harmonic suppression capability. Therefore, the controller gain k determined in this embodiment is r The value of is 10.

[0140] In this embodiment, a single-phase grid-connected inverter experimental platform based on DSP28335 is used to compare and verify the traditional repetitive control (RC), odd-order repetitive control (ORC) and the nested odd-order repetitive proportional control (NORC-PC) of the present invention at different grid frequencies. The grid-connected current THD of the three control strategies is as follows: Figure 15 shown.

[0141] In this embodiment, the experimental parameters of the single-phase grid-connected inverter experimental platform used are shown in Table 1.

[0142] Table 1 Parameters of single-phase LCL grid-connected inverter

[0143]

[0144] Depend on Figure 15 It can be seen that when the grid frequency f0 fluctuates, the THD values ​​of the grid-connected current under the three control strategies of RC, ORC and NORC-PC all increase to varying degrees, but all remain within the allowable range of 5%. Among them, when the grid frequency f0 = 50Hz, the THD of the grid-connected current under the above three control strategies is the smallest, and the harmonic suppression capability under the NORC-PC control strategy is the best. Specifically, when the grid frequency f0 = 50Hz, the grid-connected current and its spectrum of the traditional repetitive control (RC) are as follows: Figure 16 As shown, the grid-connected current and its spectrum of odd repetitive control (ORC) are as follows Figure 17 As shown, the grid-connected current and its spectrum of the nested odd-order repetitive proportional control internal model (NORC-PC) of the method of the present invention. The grid-connected current and its spectrum of the above three control strategies are shown as follows: Figure 18 shown.

[0145] By comparing the current and spectral characteristics of the three control strategies of RC, ORC and NORC-PC, the nested odd-order repetitive proportional controller (NORC-PC) of the present invention can demonstrate better harmonic suppression capability when the grid frequency shifts. At the same time, NORC-PC performs outstandingly in frequency adaptability, verifying its strong robustness when the grid frequency fluctuates.

[0146] The present invention adopts a nested odd-repetition proportional control strategy and sets an internal model formed by two odd-repetition controls, thereby improving the harmonic suppression capability and strong robustness in dealing with grid frequency fluctuations, breaking through the limitations of traditional control strategies in terms of harmonic suppression range, and significantly improving the system's stable operation capability under non-ideal conditions, providing a more excellent solution for grid-connected inverter control in complex grid conditions.

[0147] In this embodiment, the controlled object may also be an industrial device whose output voltage / current signal is composed of odd-order characteristic power, including a programmable AC power supply, a power converter, and a servo motor.

[0148] The present invention further provides a nested odd-repetition proportional controller, which is implemented by the above-mentioned nested odd-repetition proportional controller design method.

[0149] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection defined by the claims.

Claims

1. A nested odd-order repetitive proportional controller design method, characterized by: The following steps are involved: S1: Determine the transfer function P(s) of the controlled object; S2: Construct nested odd-order repetitive control internal model; The nested odd-repetition control internal model includes an external odd-repetition control internal model and an internal odd-repetition control internal model that are nested. The internal odd-repetition control internal model G iorc (z) Insert the odd repetition control inner model G in the outer norc (z), its expression is: Among them, γ1 and γ2 are the first internal model coefficient and the second internal model coefficient of the internal odd-order repetitive control internal model, k r is the internal model gain; S3: Add a phase lead compensator and a system compensator to the nested odd-order repetitive control internal model to construct a nested odd-order repetitive controller, whose discrete transfer function G2(z) is: Among them, z m is the phase advance compensator, S(z) is the system compensator; S4: Add a feedforward controller to the nested odd-order repetitive controller G2(z) for the controlled object P(s) to obtain a nested odd-order repetitive proportional controller, whose output y(z) is expressed as follows: Among them, r(z) is the reference signal, d(z) is the disturbance signal, k p is the proportional gain of the feedforward controller, P(z) is converted from P(s) using the zero-order hold method; The transfer function P0(z) of the controlled object under the control of the feedforward controller is expressed as: S5: Design and select nested odd-repetition proportional control parameters to form a stable nested odd-repetition proportional control system, that is, the characteristic equation of the nested odd-repetition proportional control system (1+k p P(z))(1+G2(z)P0(z)) satisfies the first stability condition and the second stability condition, The first stability condition is: 1+k p All roots of P(z) are inside the unit circle centered at the origin; The second stability condition is: |1+G2(z)P0(z)|≠0.

2. The nested odd-repetition ratio controller design method according to claim 1, characterized in that: The proportional gain k in step S4 p The method to determine is: Selecting a proportional gain value within a preset proportional gain range, and constructing a Bode diagram of the transfer function P0(z) of the controlled object under the control of the feedforward controller corresponding to different proportional gain values; Determine the proportional gain k when the first stability condition is met based on the Bode diagram p .

3. The nested odd-repetition ratio controller design method according to claim 1, characterized in that: The internal odd repetition control internal model G iorc The method to determine is: Select the first internal model coefficient value within the preset first internal model coefficient range, select the second internal model coefficient value within the preset second internal model coefficient range, and construct the G corresponding to different first internal model coefficient values ​​and second internal model coefficient values. iorc The Bode plot of (z), According to the Bode diagram, the first internal model coefficient γ1 and the second internal model coefficient γ2 are determined, and then the internal odd-order repetitive control internal model G is determined. iorc .

4. The nested odd-repetition ratio controller design method according to claim 1, characterized in that: The system compensator S(z) adopts a fourth-order Butterworth low-pass filter with a cutoff frequency of 1 kHz, and its transfer function is:

5. The nested odd-repetitive ratio controller design method according to claim 1, characterized in that: The step S5 further includes: obtaining the controller gain k according to the second stability condition. r and phase lead compensator z m The condition of the parameter m, the controller gain k r The conditions are: The phase lead compensator z m The conditions for the parameter m are: |θ s (w)+θ p (w)+mw|<90°。 6. The design method of a nested odd-order repetitive ratio controller according to claim 5, characterized in that: The phase lead compensator z m The method to determine is: According to the phase advance compensator z m The conditions of the parameter m, constructing θ when different parameter m values s (w)+θ p The Bode diagram of (w)+mw is used to select the value of the parameter m.

7. The design method of a nested odd-repetitive ratio controller according to claim 5, characterized in that: The controller gain k r The method to determine is: According to the second stability condition, let H(z)=Q(z)(1-k r z m S(z)P0(z)); Where z = e jwt , according to the controller gain k r Under the conditions, different controller gains k are constructed r When H(e jwt ) Nyquist curve, and determine k according to the Nyquist curve r The value of .

8. The nested odd-repetitive ratio controller design method according to claim 1, characterized in that: The controlled object is an industrial device whose output voltage / current signal is composed of odd-order characteristic power, including a programmable AC power supply, a power converter and a servo motor.

9. The nested odd-repetitive ratio controller design method according to claim 1, characterized in that: The controlled object is an LCL filter, and the transfer function P(s) of the controlled object is: Among them, L1 is the filter inductor on the inverter side, L2 is the filter inductor on the grid side, C is the filter capacitor, and R is the damping resistor.

10. A nested odd-repetition proportional controller, characterized in that: The controller is implemented by the nested odd-repetitive proportional controller design method described in any one of claims 1-9.

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